\section{Introduction}

\frame{
  \frametitle{Outline}
  \tableofcontents[sectionstyle=show/shaded,subsectionstyle=hide]
}

\subsection{Goal \& Motivation}

\frame[t] {
  \frametitle{Overview}
  \begin{objective}
    Achieve robust humanlike bipedal robotic walking in simulation on rough terrain.
  \end{objective}

  We achieve this by:

  \begin{itemize}
    \item Constructing a hybrid model of the biped
    \item Design a humanlike trajectory with Human-Inspired Control
    \item Linearizing the dynamics at points along the designed trajectory
    \item Constructing Linear Quadratic Regulators for each linear system
    \item Simulating the nonlinear system on various terrains
  \end{itemize}
}

\frame[t]{
  \frametitle{History}

  \begin{columns}[T]
    \begin{column}{.24\textwidth}
      \textcolor{blue}{Passive \\ Walking:}
      \begin{figure}
        \centering
        \includegraphics[height=4cm]{passivewalker}
      \end{figure}
    \end{column}

    \begin{column}{.24\textwidth}
      \textcolor{blue}{Passivity-based Control:}
      \vspace{-4mm}
      \begin{figure}
        \centering
        \includegraphics[height=4cm]{collins}
      \end{figure}
    \end{column}

    \begin{column}{.24\textwidth}
      \textcolor{blue}{Hybrid Zero Dynamics:}
      \begin{figure}
        \centering
        \includegraphics[height=4cm]{rabbit}
      \end{figure}
    \end{column}

    \begin{column}{.24\textwidth}
      \textcolor{blue}{Human-Inspired Control}
      \vspace{1mm}
      \begin{figure}
        \centering
        \includegraphics[height=4cm]{amber_robot}
      \end{figure}
    \end{column}
  \end{columns}
}

\frame[t] {
  \frametitle{Selected Literature}
  Biomechanics researchers usually study human forces and dynamics
  \begin{itemize}
  \item
    Winter, 1990
  \item
    Perry and Burnfield, 2010
  \end{itemize}

  Roboticists study walking using hybrid models and control
  \begin{itemize}
  \item
    McGeer, 1990
  \item
    Grizzle et al, 2001
  \item
    Braun and Goldfarb, 2009
  \item
    Sinnet and Ames, 2009
  \end{itemize}

  Rough terrain results are recent
  \begin{itemize}
    \item Byl and Tedrake, 2008
  \end{itemize}
  
  Trajectory tracking has been well-studied
  \begin{itemize}
    \item Divilbiss and Wen, 1997
  \end{itemize}
}

%\frame[t]{
%  \frametitle{The Human Dynamical Control System}
%  \only<1>{
%    \vspace{-5mm}
%    \begin{figure}
%      \centering
%      \caption{Human-Inspired Control focuses on choosing output functions:}
%      \vspace{-2mm}
%      \includegraphics[height=0.75\textheight]{humancontrol2}
%    \end{figure}
%  }
%
%  \only<2>{
%    \vspace{-5mm}
%    \begin{figure}
%      \centering
%      \caption{Following human outputs yields humanlike walking:}
%      \vspace{-2mm}
%      \includegraphics[height=0.75\textheight]{humaninspiredcontrol_Part4}
%    \end{figure}
%  }
%}
